Example 1: Same R, different dollars
Trader A risks twenty dollars on a trade and makes sixty; trader B risks two thousand on another and makes six thousand. In dollars they look incomparable, but both made plus three R: each made three times what they risked. If you only saw the dollars you might think B traded far better, when in R terms the two trades were identical in quality. Measuring in R is what lets you see that, and lets a single trader compare a small probe to a full-size position on the same scale.
